Oct 13, 2015 · So I have the following graphs drawn. How can I tell whether they are bipartite? If it is bipartite, how to identify 2 disjoint non empty sets?

A theorem of König says that Any bipartite graph G G has an edge-coloring with Δ(G) Δ (G) (maximal degree) colors. This document proves it on page 4 by: Proving the theorem for regular bipartite …

Jun 7, 2020 · Of course, the definition of "bipartite" is easily generalised to graphs that are not simple, and we might want to do this in some cases: for instance if we are studying graph colourability, we …

Jan 24, 2016 · Can someone explain to me with an example how to create the adjacency matrix of a bipartite graph? And why the diagonal elements of it are not zero? Thanks.

Dec 8, 2017 · If the graph really is bipartite, P P now contains a complete partition of the graph. Permute the adjacency matrix to put all the members of P P first, and all of the members of Q Q last.

How can we prove that a graph is bipartite if and only if all of its cycles have even order? Also, does this theorem have a common name? I found it in a maths Olympiad toolbox.

Dec 10, 2025 · Take the bipartite complement of our vertex-transitive bipartite graph: toggle all edges between A A and B B. This will be another vertex-transitive bipartite graph, and now we are looking …

Jul 24, 2024 · A bipartite graph has a unique bipartition (except for interchanging the two partite sets) if and only if it is connected. Let G be a bipartite graph. If u and v are vertices in distinct components, …

Jan 29, 2015 · I thought a constraint would be that the graphs cannot be complete, otherwise the complements would be disconnected. but, if I take a bipartite graph with 4 vertices on each side, and …

Jul 27, 2016 · Prove that all trees are bipartite [closed] Ask Question Asked 9 years, 5 months ago Modified 7 months ago